Multiple types of graph products exist, that is, we can enforce connections across modes in different ways [1]}. In the case of the Cartesian product as in Figure 1(b), the measurement of the \(n^{th}\)  sensor at the \(k^{th}\)  time step is related to not only to its neighboring sensors at the \(k^{th}\)  time step but also to its measurements at the \((k-1)^{th}\)  and \((k+1)^{th}\)  time steps respectively. Hence, constructing a framework for efficient sampling and recovery on such product graphs is an important step for tasks such as graph signal recovery, compression, and semi-supervised learning on large-scale and multi-modal graphs.
